Finite Group Databasebeta

C2×C4×#14523232 #30647139

order16256
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#14523232

Splittings

SylowC127 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC2×C42C2×D127
commutatorC2×C127C22×C42
FrattiniC2×C4C23×D127
FittingC22×C42×C127C2
socleC23×C127C22×C4
prime radicalC24×C127C2×C4
cosocleC2×C4×C127C24
hypercenterC22×C42D127
hypocenterC127C2×C4×M16
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C42 ◁ C22×C42

656 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 12919);